The invention relates generally to determinations of the remaining useful life of structures and structural elements. More particularly, the invention relates to methods and apparatus enabling the nonlinear detection of imminent structural failure due to induced crack growth.
Structural elements of any kind are subject to a variety of stresses that will ultimately result in the failure of the element. Examples of stresses are tensile, flexure, or shear stresses resulting from applied loads, the loads being either (a) statically or (b) regularly or irregularly periodically applied. Environmental corrosion can also constitute a stress to the structure. The applied load and environmental stresses, each acting separately or in combination, result in the creation and propagation of cracks in the structural element. The proliferation of cracks eventually causes the failure of the element.
It has long been a goal of those concerned with the useful life and eventual failure of structural elements to accurately predict the imminent failure of such elements. A primary consideration is safety, inasmuch as the failure of an element in, for example, a bridge or a mechanism such as a train car, can have a direct effect on the safety of people using the bridge or riding the train. A second significant concern is economics. While allowing a structural element to approach too closely its estimated time of failure creates the risk of an earlier than expected failure, which is a significant safety risk, repairing or replacing the element too early in its useful life is expensive. Utilizing too large a safety factor can waste a significant portion of the actual useful life of the element, contributing to higher costs for the element and/or the structure of which it is a part.
One type of failure of a structural element is tensile fatigue failure. Tensile fatigue causes the propagation of fatigue cracks, and hence to failure of the element. An analytically simple method of predicting tensile fatigue failure due to fatigue crack growth is to subject a statistically significant number of the structural element in question to empirical and/or experimental end-of-life (EOL) testing. This involves testing to destruction under stress conditions intended to duplicate those expected to be found in actual use. The results enable a determination of a mean value for and the variability in actual time to failure for a given set of loading, frequency, and environmental conditions. A predetermined safety factor can be incorporated in a prediction of structural service life to balance safety against utilizing as much of the useful life of the element as possible.
This method and equivalent methods for predicting failure due to other types of stress, however, are cumbersome, expensive, and time-consuming. Moreover, in the aforementioned fatigue failure method, for example, the material property determination of a mean value and the variability of the number of cycles to failure is also affected by the nature and frequency of the applied loadings and the environmental conditions over the service life of the structure. In addition, for multiple loadings, it requires a knowledge of the critical type of loading. Also, where the safety is concern is very high, such as for a high speed mass transit vehicle, the predictive window provided by such tests is too broad for accurate use with a particular structural member. Imposing a high enough safety factor to counter this breadth simply results in the practical loss of useful life.
An illustrative but not limiting example relates to aircraft frames. The structural lifetime of military and civilian aircraft is ultimately limited by the airframe fatigue life. The precise prediction of the future time of failure is made very difficult because the fatigue crack growth-limited lifetimes may vary by a factor of as much as ten (10) to twenty (20). Imposing a safety factor to account for this variation results in the grounding of many aircraft at times that are far short of the inherent fatigue lifetime thereof in an attempt to limit the possibility of fatigue failure in the theoretically weakest airframe in the fleet.
Prior to about the late 1970""s, the design criteria for airframe fatigue life, known as xe2x80x9csafe life,xe2x80x9d were based on experimentally-derived stress-number of cycles to failure (S-N) curves. This technique used the empirical and experimental approach addressed above, and suffers from the same drawbacks. The assumptions that must be made with regard to the effects of unknown or partially known variables in the service life of the airframe require factors of safety to be enforced on the entire fleet to account for the possible extremes in exposure of some members of the fleet. That is, it must be assumed that not only is every structural element as weak as the weakest element tested, but that each airframe will encounter the worst possible environment with respect to adverse effects on the member.
Designers of military aircraft next adopted a fracture mechanics approach, also referred to as xe2x80x9cdamage tolerance.xe2x80x9d This method is based on measuring the size of existing cracks in a structural element. Predictive calculations based on these measurements are used to estimate the remaining useful life of the element. Many civilian and military aircraft now nearing the specified airframe lifetimes, however, were designed and built prior to the use of fracture mechanics as design tools. Assessing these aircraft now with a view to using fracture mechanics involves a time and cost prohibitive evaluation. Moreover, even an exhaustive evaluation cannot determine the stress and fatigue history of the structural elements, which makes any predictive calculations inherently suspect. Finally, certain needed variables, such as initial stress resistance and other factors, were simply not measured or calculated for the existing airframes, creating a situation in which predictions either cannot be made or in which certain variables must to themselves be estimated. This adds, of course, an entirely separate degree of uncertainty to the use of this methodology on existing elements. These aircraft now face premature retirement because there are no tools and methods available to assure continued safe operation with confidence.
The current method of crack growth measurement requires periodic, costly nondestructive evaluation (NDE) of these existing airframes and the constituent elements, and concomitant meticulous record keeping to record and track crack growth. The current method also suffers from the inherent uncertainties stated above. In addition, these uncertainties are compounded by three known and routinely encountered factors. First, where multiple cracks are created and are propagated, the stress fields of the multiple cracks can and will interact with each. This interaction makes a determination of a critical crack size, with respect to failure, very difficult. Also, a given structural element is subject to widely varying types and magnitudes of loadings, and in the presence of widely varying degrees of corrosive environments. The compounding nature of these variations makes analytical predictions based on fracture mechanics sufficiently imprecise that, again, large factors of safety are required. These factors introduce variables for which the current methods can only compensate for by introducing large factors of safety, or by requiring additional loading and environmental exposure record keeping. Moreover, it is known that overstress to an element tends to slow, at least temporarily, the rate of crack growth. This is analytically difficult inasmuch as there is no means of detecting, predicting, and accounting for either the overstress or the existence and extent of the slowing. Other variables also affect the method, of which the foregoing are well-known examples.
Thus, despite the need for and importance of accurately predicting failure caused by crack growth, existing methods are cumbersome, expensive, and time-consuming. There are also uncertainties for which no adjustment is currently available. Finally, current methods rely in whole or in part on statistical calculations for a set of elements, rather than for the single element in question. The predictive xe2x80x9cwindowxe2x80x9d or interval is thus unacceptably large, leading to structural elements being taken out of service long before the actual end of the useful life thereof. Methodologies providing an improved prediction and thus a higher level of confidence, and apparatus to implement the methodologies, are needed. In addition, methods and apparatus for monitoring individual elements are needed to aid in the task of significantly narrowing the predictive interval of failure.
It is an object of this invention to provide a method and apparatus for detecting and providing an indication of imminent failure in a structural element.
It is a further object of this invention to provide a method and apparatus for monitoring changes in crack growth rate in structural materials.
It is another object of this invention to provide a method and apparatus for manipulating data in real time to provide a detection of a given stage of crack growth in a structural element where the crack growth is induced by loading, creep, stress, corrosion or a combination thereof.
It is also an object of this invention to provide a method for converting physical data from a structural element into a measure at least proportional to crack growth rate.
Another object of the invention is to provide a method and apparatus for relating crack growth rates in structural elements to an indication of the imminent failure of the elements.
Still another object of this invention is provide a method and apparatus incorporating a unique nonlinear filter for crack growth-related data to enable the accurate detection of significant changes in such data.
It is likewise an object of this invention to provide apparatus for detecting loading and stress factors for a structural element and for creating as an output an indication of the structural status for the structural element.
It is moreover an object of this invention to provide apparatus including sensors associated with a structural element from which data is received and manipulated to provide an indication related to the end of service life for the structural element.
It is also an object of this invention to provide a method and apparatus for monitoring crack growth rate-related data in structural elements to provide an indication of the accelerating crack growth rate indicative of the imminent approach of the end of service life for the structural element.
It is a further object of this invention to provide a method and apparatus for converting load and displacement data for a structural element to a measure of time-dependent absorbed strain energy as a means of monitoring and measuring the rate of crack growth within the structural element.
It is an object of this invention to accomplish the foregoing method and provide the foregoing apparatus in a manner incorporating nonlinear filtering means to monitor crack growth in structural elements and provide an indication of imminent failure in such elements due to such crack growth.
These and other objects of the invention are achieved by providing a method for the nonlinear prediction of failure in a structural element subject to a load, the method including the steps of sensing load- and strain-related data for said structural element, generating a crack-growth function relating said load- and strain- or load- and displacement-related data to an interval, deriving from said crack-growth function at least one indicator function, monitoring trends in said at least one indicator function, and providing an indication when said monitoring detects an end-stage trend in said at least one indicator function.
These and other objects of the invention are achieved by providing a method for the nonlinear prediction of failure in a structural element subject to a load, the method including the steps of sensing load- and strain- or load- and displacement-related data for said structural element, generating a crack-growth function relating said load- and strain- or load- and displacement-related data to an interval, deriving from said crack-growth function at least one indicator function and at least one limit function, monitoring said at least one indicator function and said at least one limit function, and providing an indication when said at least one indicator function and said at least one limit function converge.
These and other objects of the invention are also provided by an apparatus for predicting failure of a structural member, said apparatus having at least one sensor for sensing load- and strain- or load- and displacement-related data representative of a load and strain to which said member is subject; interval counting means for counting a desired interval and providing an interval count associated with said load- and strain- or load- and displacement-related data; processor means operatively connected to said sensor means and said interval counting means for providing a crack growth function relating said load- and strain- or load- and displacement-related data to said interval count; processor means for deriving from said crack growth function at least one indicator function; means for monitoring said at least one indicator function and detecting trends in said function; and output means providing an indication when said monitoring means detects the onset of an end-stage trend in said at least one indicator function.
These and other objects of the invention are also provided by an apparatus for predicting failure of a structural member, said apparatus having at least one sensor for sensing load- and strain- or load- and displacement-related data representative of a load and strain to which said member is subject; interval counting means for counting a desired interval and providing an interval count associated with said load- and strain- or load- and displacement-related data; processor means operatively connected to said sensor means and said interval counting means for providing a crack growth function relating said load- and strain- or load- and displacement-related data to said interval count; processor means for deriving from said crack growth function at least one indicator function and at least one limit function; means for monitoring and comparing said at least one indicator function and said at least one limit function; and output means providing an indication when said at least one indicator function and said at least one limit function converge.